Roy Hodgson allayed fitness concerns over captain Steven Gerrard ahead of the start of the World Cup.
England begin their campaign against Italy in Manaus on Saturday and part of the build-up has been centred on fitness issues.
Alex Oxlade-Chamberlain injured his knee against Ecuador last week, while there were reports that Gerrard has been complaining of a tight groin.
The former has been stepping up his work on the training field over recent days and, according to Hodgson, there are no worries about the latter.
"We did a training session (yesterday) where the players who didn't play on Saturday (against Honduras) trained, and some of the others did a warm-down session," he said.
"Steven did some extra work at the end of that training session. There's nothing wrong with him and I don't understand that story at all."
On Oxlade-Chamberlain he said: "He's done very well and will work on his training programme during the course of the week."
"It looks very unlikely that we'll replace him (Oxlade-Chamberlain). I don't think that will be the case.
"He has got a strained medial ligament, but he is certainly working very hard and I don't think he could be further forward in terms of his progression than he is now. He's well up there."
Initial estimates put Oxlade-Chamberlain's recovery time at between two and three weeks.
That would rule Oxlade-Chamberlain out of England's first two matches, although he could feature in the final Group D game against Costa Rica and the knockout stages should the team progress.